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Banach function spaces done right
Full text linkIn this survey, we discuss the definition of a (quasi-)Banach function space. We advertise the original definition by Zaanen and Luxemburg, which does not have various issues introduced by other, subsequent definitions. Moreover, we prove versions of well-known basic properties of Banach function spaces in the setting of quasi-Banach function spaces.FJC2021-046837-
Control co-design for wave energy farms: Optimisation of array layout and mooring configuration in a realistic wave climate
Full text linkThis paper presents a novel Control Co-Design (CCD) methodology aimed at economically optimising the layout of wave energy converter (WEC) arrays. CCD ensures the synergy of optimised WEC and array parameters with the final control strategy, resulting in a comprehensive and efficient design of the array. By integrating a spectral-based control strategy into the array layout design, this study pursues the twin objectives of maximising energy absorption while reducing costs. To prove the performance of the proposed CCD methodology, an application case is proposed where the inter-device distance, alignment, and mooring configuration of a five-device array, considering realistic wave scenarios, are optimised. Energy capture and system cost evaluations are conducted, with results emphasising the significance of incorporating advanced control strategies in the design phase to improve energy absorption and reduce costs. With the application case, the study demonstrates that the optimal layout of a WEC array considering economic factors may differ from the optimal from purely technical factors, such as energy absorption, in the analysed case
Strongly coupled fermionic probe for nonequilibrium thermometry
Full text linkWe characterise the measurement sensitivity, quantified by the quantum Fisher information (QFI),
of a single-fermionic thermometric probe strongly coupled to the sample of interest, a fermionic
bath, at temperature T. For nonequilibrium protocols, in which the probe is measured before
reaching equilibrium with the sample, we find new behaviour of the measurement sensitivity
arising due to non-Markovian dynamics. First, we show that the QFI displays a highly
non-monotonic behaviour in time, in contrast to the Markovian case where it grows
monotonically until equilibrium, so that non-Markovian revivals can be exploited to reach a higher
QFI. Second, the QFI rate is maximised at a finite interrogation time t
∗
, which we characterize, in
contrast to the solution t
∗ → 0 known in the Markovian limit (Pavel Sekatski and Martí
Perarnau-Llobet 2022 Quantum 6 869). Finally, we consider probes make up of few fermions and
discuss different collective enhancements in the measurement precision
Targeting the high frequency tail of wave spectra for energy harvesting in marine sensor networks
Full text linkWhile the conventional philosophy of wave energy conversion is to target the large amounts
of power in the peak of the input wave spectrum, this study proposes that for the application of
powering marine sensor networks (MSNs), it is advantageous to target the high frequency tail of the
wave spectrum. This strategy is predicated on two primary advantages: the spatial and temporal
persistence of the wave energy resource in the high-frequency region and its compatibility with
the resonance characteristics of smaller MSN devices. The research seeks to identify the frequency
range in sea spectra which is temporally and spatially omnipresent in the marine environment,
and quantify the energy content available within this range. Theoretical frameworks are combined
with a detailed case study to analyse the temporal and spatial variations of the wave resource and
the persistent energy content in the high-frequency tail. Results reveal a notable consistency in
energy availability above 2.5 rad/s, highlighting the high-frequency tail's potential as a reliable
energy resource for MSNs. The available power in the identi ed high-frequency range is quanti ed,
providing valuable insights for the design and implementation of e cient wave energy harvesters
speci cally tailored to the needs of diverse marine environments.PRTR-C17.I
COLENGTH, MULTIPLICITY, AND IDEAL CLOSURE OPERATIONS II
No full textLet (R,m) be a Noetherian local ring. This paper concerns several extremal
invariants arising from the study of the relation between colength and (Hilbert–Samuel or
Hilbert–Kunz) multiplicity of an m-primary ideal. We introduce versions of these invariants
by restricting to various closures and “cross-pollinate” the two multiplicity theories by asking
for analogues invariants already established in one of the theories.
On the Hilbert–Samuel side, we prove that the analog of the St¨uckrad–Vogel invariant
(that is, the infimum of the ratio between the multiplicity and colength) for integrally closed
m-primary ideals is often 1 under mild assumptions. We also compute the supremum and
infimum of the relative drops of multiplicity for (integrally closed) m-primary ideals. On
the Hilbert–Kunz side, we study several analogs of the Lech–Mumford and St¨uckrad–Vogel
invariants
SINGULAR MULTIPLIERS ON MULTISCALE ZYGMUND SETS
No full textThese sets Ξ are exactly those enjoying a scale invariant version of Zygmund's (LlogL‾‾‾‾‾√,L2) improving inequality with X in place of the former space, which is termed multiscale Zygmund property. Our methods actually yield sparse and quantitative weighted estimates for the Fourier multipliers Tm and for the corresponding square functions.
In particular, our framework covers the case of singular sets Ξ of finite lacunary order and thus leads to modular and quantitative weighted versions of the classical endpoint theorems of Tao and Wright for Marcinkiewicz multipliers. Moreover, we obtain a pointwise sparse bound for the Marcinkiewicz square function answering a recent conjecture of Lerner. On the other hand, examples of non-lacunary sets enjoying the multiscale Zygmund property for each X=Lp, 1<p≤2 are also covered.
The main new ingredient in the proofs is a multi-frequency, multi-scale projection lemma based on Gabor expansion, and possessing independent interest
WEIGHTED WEAK-TYPE BOUNDS FOR MULTILINEAR SINGULAR INTEGRALS
Full text linkWe establish analogs of sharp weighted weak-type bounds for m-sublinear operators satisfying sparse form domination, including multilinear Caldero ́n-Zygmund singular integrals. Our results, which hold for general p⃗ ∈ [1, ∞)m and feature quanti- tative improvements, rely on new local testing conditions and good-λ inequalities. We address weak-type bounds in both the change of measure and multiplier settings
ENDPOINT WEAK-TYPE BOUNDS BEYOND CALDERO ́N-ZYGMUND THEORY
Full text linkWe prove weighted weak-type (r,r) estimates for operators satisfying (r,s) limited-range sparse domination of lq-type. Our results contain improvements for op- erators satisfying limited-range and square function sparse domination. In the case of operators T satisfying standard sparse form domination such as Calder ́on-Zygmund op- erators, we provide a new and simple proof of the sharp bound
∥T∥L1 (Rd)→L1,∞(Rd) [w]1(1 + log[w]FW)
Nonlocal cooperative behaviour, psychological effects, and collective decision-making: an exemplification with predator-prey models
Full text linkIn bio-social models, cooperative behaviour has evolved as an adaptive strategy, playing multi-functional
roles. One of such roles in populations is to increase the success of survival and reproduction of individuals and their families or social groups. Moreover, collective decision-making in cooperative behaviour
is an aspect that is used to study the dynamic behaviour of individuals within a social group. In this
paper, we have focused on population dynamics by considering a predator-prey model as our main exemplification, where the generalist predator has adopted a cooperative hunting strategy while consuming
their prey. In particular, we have analyzed the dynamic nature of the system when a nonlocal term
is introduced in the cooperation. First, the Turing instability condition has been studied for the local
model around the coexisting steady-state, followed by the Turing and non-Turing patterns in the presence of the nonlocal interaction term. This work is also concerned with the existence of travelling wave
solutions for predator-prey interaction with the nonlocal cooperative hunting strategy. Such solutions
are reported for local as well as for nonlocal models. We have characterized the invading speed of the
predator with the help of the minimal wave speed of travelling wave solutions connecting the predatorfree state to the co-existence state. The travelling waves are found to be non-monotonic in this system.
The formation of wave trains has been demonstrated for an extended range of nonlocal interactions.
Finally, the importance of psychological effects in shaping the dynamics of nonlocal collective behaviour
is demonstrated with several representative examples
Reliable prediction of difficult airway for tracheal intubation from patient preoperative photographs by machine learning methods
Full text linkBackground:
Estimating the risk of a difficult tracheal intubation should help clinicians in better anaesthesia planning, to maximize patient safety. Routine bedside screenings suffer from low sensitivity.
Objective:
To develop and evaluate machine learning (ML) and deep learning (DL) algorithms for the reliable prediction of intubation risk, using information about airway morphology.
Methods:
Observational, prospective cohort study enrolling =623 patients who underwent tracheal intubation: 53/623 difficult cases (prevalence 8.51%).
First, we used our previously validated deep convolutional neural network (DCNN) to extract 2D image coordinates for 27 + 13 relevant anatomical landmarks in two preoperative photos (frontal and lateral views). Here we propose a method to determine the 3D pose of the camera with respect to the patient and to obtain the 3D world coordinates of these landmarks. Then we compute a novel set of =59 morphological features (distances, areas, angles and ratios), engineered with our anaesthesiologists to characterize each individual's airway anatomy towards prediction.
Subsequently, here we propose four ad hoc ML pipelines for difficult intubation prognosis, each with four stages: feature scaling, imputation, resampling for imbalanced learning, and binary classification (Logistic Regression, Support Vector Machines, Random Forests and eXtreme Gradient Boosting). These compound ML pipelines were fed with the =59 morphological features, alongside =7 demographic variables. Here we trained them with automatic hyperparameter tuning (Bayesian search) and probability calibration (Platt scaling). In addition, we developed an ad hoc multi-input DCNN to estimate the intubation risk directly from each pair of photographs, i.e. without any intermediate morphological description.
Performance was evaluated using optimal Bayesian decision theory. It was compared against experts' judgement and against state-of-the-art methods (three clinical formulae, four ML, four DL models).
Results:
Our four ad hoc ML pipelines with engineered morphological features achieved similar discrimination capabilities: median AUCs between 0.746 and 0.766. They significantly outperformed both expert judgement and all state-of-the-art methods (highest AUC at 0.716). Conversely, our multi-input DCNN yielded low performance due to overfitting. This same behaviour occurred for the state-of-the-art DL algorithms. Overall, the best method was our XGB pipeline, with the fewest false negatives at the optimal Bayesian decision threshold.
Conclusions:
We proposed and validated ML models to assist clinicians in anaesthesia planning, providing a reliable calibrated estimate of airway intubation risk, which outperformed expert assessments and state-of-the-art methods. Our novel set of engineered features succeeded in providing informative descriptions for prognosis